cohomology group


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cohomology group

[′kō·hə′mäl·ə·jē ‚grüp]
(mathematics)
One of a series of Abelian groups Hn (K) that are used in the study of a simplicial complex K and are closely related to homology groups, being associated with cocycles and coboundaries in the same manner as homology groups are associated with cycles and boundaries.
References in periodicals archive ?
N,S]) consisting of those homomorphisms which induce isomorphisms between the respective Tate cohomology groups of [X.
Then the 2-th Hochschild cohomology group of A with coefficients in X is defined by
Again, if w is not a coboundary, then there is no ample division algebra in C(G,[omega],R); if w is a coboundary, then the iso-classes of ample division algebras in C(G,[omega],R) with D = R or H are parametrized by the second cohomology group [H.
We wish to construct equivariant Chern classes for Real bundles in equivariant cohomology groups with integral coefficients and our main requirement is that one recovers the classical Chern classes by forgetting the [C.
An important connection between the cohomology groups of finite dimensional CSL-algebras (with values in the enveloping matrix algebras) and the homology groups of certain simplicial complexes was presented recently by Kraus and Schack [18].
MacLane and Whitehead have proved in [MW] that equivalence classes of so called crossed modules are in bijection with the elements of the third cohomology group [H.
2]), r < d, be the first nonzero reduced cohomology group of M.
D])= -2 so that the last cohomology group must have positive dimension.
Section 3 contains the proprieties of two-dimensional local field we need, such as, duality and the vanishing of the second cohomology group.
Among the topics are genus change in inseparable extensions of functional fields, the homology of noetherian rings and local rings, the cohomology groups of tori in infinite Galois extensions of number fields, an algorithm for determining the type of a singular fiber in an elliptic pencil, variation of the canonical height of a point depending on a parameter, the non-existence of certain Galois extensions of Q unramified outside two, and refining Gross' conjecture on the values of abelian L-functions.
Basic forms are preserved by the exterior derivative and are used to define basic de-Rham cohomology groups [H*.
The endomorphism algebra of a tilting module preserves many significant invariants, for example, the center of an algebra, the number of nonisomorphic simple modules, the Hochschild cohomology groups, and Cartan determinants.